Understanding the dynamics of microearthquakes is a timely challenge with the potential to address current paradoxes in earthquake mechanics, and to better understand earthquake ruptures induced by fluid injection. We perform fully 3D dynamic rupture simulations caused by fluid injection on a target fault for FEAR experiments generating Mw ≤ 1 earthquakes. We investigate the dynamics of rupture propagation with spatially variable stress drop caused by pore pressure changes and assuming different constitutive parameters. We show that the spontaneous arrest of propagating ruptures is possible by assuming a high fault strength parameter S, that is, a high ratio between strength excess and dynamic stress drop. In faults with high S values (low rupturing potential), even minor variations in Dc (from 0.45 to 0.6 mm) have a substantial effect on the rupture propagation and the ultimate earthquake size. Our results show that modest spatial variations of dynamic stress drop determine the rupture mode, distinguishing self-arresting from run-away ruptures. Our results suggest that several characteristics inferred for accelerating dynamic ruptures differ from those observed during rupture deceleration of a self-arresting earthquake. During deceleration, a decrease of peak slip velocity is associated with a nearly constant cohesive zone size. Moreover, the residual slip velocity value (asymptotic value for a crack-like rupture) decreases to nearly zero. This means that an initially crack-like rupture becomes a pulse-like rupture during spontaneous arrest. In summary, our findings highlight the complex dynamics of small earthquakes, which are partially contrasting with established crack-like models of earthquake rupture.